Two-stage structural damage detection using modal strain energy and natural frequencies: Numerical and experimental study

The present study suggests a new damage index using natural frequency and modal strain energy called NFMSEBI for two-stage structural damage localization and quantification. The goal is to improve the performance of conventional modal strain energy-based index (MSEBI) for damage localization of different structures. For this purpose, three different structures including a planar frame, a planar truss, and an experimental 6-story shear frame were studied. For the optimization stage, three different objective functions are suggested using the combination of mode shapes and natural frequencies, generalized flexibility matrix and natural frequencies, and static displacements and natural frequencies. The performance of the mentioned objective functions is compared utilizing a nature-based metaheuristic algorithm named marine predator algorithm (MPA). Moreover, the performance of MPA has been compared to that of artificial hummingbird algorithm (AHA) and arithmetic optimization algorithm (AOA) using the most accurate objective function selected for each structure. The results showed that the influence of damage is more reflected in NFMSEBI than in MSEBI, whereas in some cases of the planar frame, MSEBI failed to identify damaged elements. Furthermore, the first objective function produces the most accurate results for the truss and frame models, while the second one produces the most reliable identifications for the experimental structure. For the experimental structure MPA and AHA have superior performance over AOA, while in numerical models MPA has the most accurate and stable results.